is stone take longer for the downward motion than, Physics

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is stone take longer for the downward motion than

Is stone take longer for the downward motion than for the upward motion

Consider a stone thrown vertically upward. if we take friction against air into account, we see that the mechanical energy(1/2mv^{^}2+ mgy) must decrease as a function of time. From this prove that the stone will take longer for the downward motion than for the upward motion

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